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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Carnot's theorem ： ウィキペディア英語版 Carnot's theorem In Euclidean geometry, Carnot's theorem states that the sum of the signed distances from the circumcenter ''D'' to the sides of an arbitrary triangle ''ABC'' is :$DF\; +\; DG\; +\; DH\; =\; R\; +\; r,\backslash$ where ''r'' is the inradius and ''R'' is the circumradius of the triangle. Here the sign of the distances is taken negative if and only if the line segment ''DX'' (''X'' = ''F'', ''G'', ''H'') lies completely outside the triangle. In the picture ''DF'' is negative and both ''DG'' and ''DH'' are positive. The theorem is named after Lazare Carnot (1753–1823). It is used in a proof of the Japanese theorem for concyclic polygons. ==External links== * * (Carnot's Theorem ) at cut-the-knot * (Yet another Carnot's Theorem with multiple applications ) at cut-the-knot * (Carnot's Theorem ) by Chris Boucher. The Wolfram Demonstrations Project. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Carnot's theorem」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.